Answers
sqrt(1-3x)=x+3
squaring both sides we get:
1-3x=(x+3)^2
1-3x=x^2+6x+9
this can be written in quadratic form as:
x^2+6x+3x+9-1=0
x^2+9x+8=0
factorizing the above we get:
x^2+9x+8=0
x^2+x+8x+8=0
x(x+1)+8(x+1)=0
(x+8)(x+1)=0
thus;
x+1=0
x=-1
and
x+8=0
x=-8
hence the answer is x=-1 or x=-8
the correct answer is A
The solution to the equation [tex]\sqrt{1-3x}= x+3[/tex] is x = -8 or x = -1.
To find the solution of the equation √(1-3x) = x+3, we can use algebraic techniques to isolate the variable x.
First, let's square both sides of the equation to eliminate the square root:
[tex](\sqrt{1-3x})^{2} = (x+3)^2[/tex]
Simplifying, we get:
[tex]1-3x = x^2 + 6x + 9[/tex]
Next, let's gather all the terms on one side of the equation:
[tex]x^2 + 6x + 9 - 1 + 3x = 0[/tex]
Simplifying further, we have:
[tex]x^2 + 9x + 8 = 0[/tex]
Now, we can factor the quadratic equation:
(x+1)(x+8) = 0
Setting each factor equal to zero, we have:
x+1 = 0 or x+8 = 0
Solving these equations, we find:
x = -1 or x = -8
Therefore, the solution to the equation [tex]\sqrt{1-3x}= x+3[/tex] is x = -8 or x = -1.
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Related Questions
For g(x)=9x^2-2x find g(-2)
Answers
First, we need to replace every 'x' with -2 as we are using the function of g(-2).
9(-2^2) - 2(-2)
Simply the parenthesis.
9(4) + 4
Simplify.
36 + 4
40 is your answer.
I hope this helps!
Doug read 231 pages in seven hours. he read the same number of pages each hour. how many pages do you read in one hour ?
Answers
Answer: 33 pages
Doug can read 33 pages in one hour.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total pages in a book= 231 pages
Time to read books= 7 hours
so, in 1 hour he can read = 231/7
= 33 pages.
Hence, he can read 33 pages in one hour.
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if 7x+3=24, find the value of -5 - 6x.
a)-23
b)-7
c)1
d)17
Answers
If 7x plus 3 equals 24, X equals 3. -5 minus 6 time X(3) equals -23.
Complete the solution of the equation. find the value of y when equals -7
-3x+6y=-21
Answers
-3x+6y=-21
-3(-7) +6y = -21
21 + 6y = -21
6y = -42
y = -7
The value of y when equals -7 would be equal to -7.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given the equation as-3x+6y=-21
if x = -7 then we get;
-3x+6y=-21
Substitute;
-3(-7) +6y = -21
21 + 6y = -21
6y = -42
y = -7
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The area of a triangular flag is 4242 square centimeters. its altitude is 2 centimeters longer than twice its base. find the lengths of the altitude and the base.
Answers
h = 2b + 2
A = 42
42 = (b(2b + 2)) / 2
42 = (2b^2 + 2b) / 2
42 = b^2 + b
b^2 + b - 42 = 0
(b + 7)(b - 6) = 0
b + 7 = 0
b = -7...nope..extraneous solution
b - 6 = 0
b = 6 <== base
h = 2b + 2
h = 2(6) + 2
h = 12 + 2
h = 14 <=== height (altitude)
A bag contains 5 apples and 3 oranges. if you select 4 pieces of fruit without looking, how many ways can you get 4 apples?
Answers
That is becasue if you do not select an apple on any of the selections then you will not have selected 4 apples, so you do not have any chance to select a different fruit.
Now, given that there are 5 apples, you can combine them in 5C4 ways:
5C4 = 5! / [(4!) (5-4)! ] = 5! / [4! * 1!] = 5 * 4! / 4! = 5
Answer: 5 ways.
Answer:
5 ways
Step-by-step explanation:
I got it correct on founders edtell
Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments.
She calculates two regression models. Which is true?
A.) The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.
B.) The linear model better represents the situation because according to the exponential model, the repayment amount will never be 0.
C.) The exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months.
D.) The exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.
Answers
2700-2110 = 590
2110-1500 = 610
1500-870 = 630
870-220 = 650
Their differences are about the same having a mean of 620. Thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve. The answer is A.
The regression models used by Jessica is such that A.) The linear model better represents the situation ... owes is decreasing by about the same amount every 6 months.
What regression model is best?The linear regression model is best for a situation where there is a constant rate of change while the exponential model is for situations where change isn't constant.
Jessica's data shows that there is a constant rate of reduction in the amount to repay because the amounts are quite similar to each other as shown by the graph.
In conclusion, option A is correct.
Find out more on linear regression at https://brainly.com/question/25987747.
(06.02 LC)
Which line best represents the line of best fit for this scatter plot?
Line P
Line Q
Line R
Line S
Answers
hope this helps:)
Answer:
The correct option is 3. Line R represents the line of best fit for this scatter plot.
Step-by-step explanation:
A straight line is called line of best fit if it minimize the sum of the squared prediction errors. It means the distance of all the points from the line is minimum.
The best fit line may or may not passes through the scatter points. Some scatter points lie above the line and some lie below the best fit line. In other words the best fit line passes through the middle points.
From the given graph it is clear that the line R passes through 3 points. The number of points above the line is equal to the number of points below the line. So, R is the line of best fit
Line R represents the line of best fit for this scatter plot. Therefore the correct option is 3.
What is the value for B, after the equation A=3/7(B-25) is rearranged?
Answers
Hope this helps!
Answer:
[tex]B=\frac{7A}{3}+25[/tex]
Step-by-step explanation:
We have been given an equation [tex]A=\frac{3}{7}(B-25)[/tex]. We are asked to find the value of B for our given equation.
Upon multiplying both sides of our equation by [tex]\frac{7}{3}[/tex], we will get:
[tex]\frac{7}{3}*A=\frac{7}{3}*\frac{3}{7}(B-25)[/tex]
[tex]\frac{7}{3}*A=B-25[/tex]
[tex]\frac{7A}{3}+25=B-25+25[/tex]
[tex]\frac{7A}{3}+25=B[/tex]
[tex]B=\frac{7A}{3}+25[/tex]
Therefore, the value of B is [tex]\frac{7A}{3}+25[/tex].
Find the area of the regular polygon.
pentagon with a radius of 4 ft
Answers
sin36∘4sin36∘8sin36∘n=.5n4=12n=n≈4.7 cos36∘=a44cos36∘=aa≈3.24
Using these two pieces of information, we can now find the area.
A=12(3.24)(5)(4.7)≈38.07 units^2.
Paul planted 20 onion bulbs. Three-fourths of the bulbs sprouted. How many onion plants did Paul have?
Answers
3/4(20) = 60/4 = 15 onion plants <=
Paul had 15 onion plants.
To solve the problem, we need to calculate three-fourths of the 20 onion bulbs that Paul planted, as this represents the number of bulbs that sprouted.
First, we find three-fourths of 20 by multiplying 20 by the fraction [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[ \frac{3}{4} \times 20 = \frac{3 \times 20}{4} \][/tex]
[tex]\[ \frac{3 \times 20}{4} = \frac{60}{4} \][/tex]
[tex]\[ \frac{60}{4} = 15 \][/tex]
Therefore, 15 onion bulbs sprouted, which means Paul had 15 onion plants.
Classify the variable as discrete or continuous. weights of backpacks of first graders on a school bus
Answers
Angle x is an acute angle in a triangle. If cos x=4/5, then the sin x=
Answers
Answer:
[tex]\bf \sin x =\frac{3}{5}[/tex]
Step-by-step explanation:
Angle x is an acute angle in a triangle.
The measure of cosine angle is given to be :
[tex]\cos x = \frac{4}{5}[/tex]
Now, we need to find the measure of the sine angle for the same triangle.
[tex]\cos x = \frac{Base}{Hypotenuse}[/tex]
⇒ Base = 4 units and Hypotenuse = 5 units
So, Length of perpendicular = 3 units ( By using Pythagoras theorem)
[tex]\sin x=\frac{Perpendicular}{Hypotenuse}\\\\\implies\bf \sin x =\frac{3}{5}[/tex]
Evaluate the expression:
the difference of 26 and 22
Select one:
a. 48
b. 91
c. 4
d. 13/11
Answers
To do this, all you have to do is subtract 22 from 26. 26-22=4.
Answer: C.) 4
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The given series has six terms. what is the sum of the terms of the series? 10 + 20 + 30 + . . . + 60 420 120 210 240
Answers
Answer:
10+20+30+40+50+60=210
Step-by-step explanation:
Let's simplify the series and then apply a useful method.
The original series is:
10+20+30+40+50+60, which can be simplified as:
10*(1+2+3+4+5+6)
Considering that you have a new series starting in 1 and the following numbers are consecutive, then the Gauss equation can be used, which is:
S=n*(n+1)/2, where n is the last value of a consecutive-number series starting in 1.
Through this equation we can find the sum of 1+2+3+4+5+6 by using:
S=6*(6+1)/2=21
Since our expression was 10*(1+2+3+4+5+6) now we can use the expression:
10*(21), obtaining the answer 210.
So, 10+20+30+40+50+60 is equal to 210.
What expression is equivalent to (4y2)^3 (3y^2)
) 12y^8
) 12y^12
)192y^8
) 192^12
Answers
If g is the number of girls in a class and b the number of boys and if there are five more girl) than boys (b) in a class, write an algebraic equation that shows this relationship.
Answers
g=b+5
b+5+b=T
2b+5=T
Evaluate [(30 + 6) − 3^2] ÷ 9 ⋅ 2
Answers
=
[(30 + 6) − 3^2] ÷ 18
=
[(30 + 6) − 9] ÷ 18
=
[36 − 9] ÷ 18
=
[27] ÷ 18
=
3/2
=
1.5
=
1 1/2
hope that helps
Solve the system by emimination 2x + 5y = 17 6x - 5y = -9
Answers
2x+5y+6x-5y=17-9
Combine like terms
8x=8
Divide
x=1
Plug the x value in
2(1)+5y=17
2+5y=17
5y=15
y=3
Final answer: (1,3)
6x - 5y = -9
----------------------add
8x = 8
x = 1
when x = 1
2x + 5y = 17
2(1) + 5y = 17
5y = 17 - 2
5y = 15
y = 3
so x = 1 and y = 3
answer
solution (1, 3)
The balance in Beth's checking account is $75. She must deposit enough money in her account to be able to pay the electric bill, which is $110. How much should she deposit?
Answers
d=$35
So she needs to deposit at least $35 to be able to pay the electric bill.
Answer:
She should deposit $35.00 in her account.
Step-by-step explanation:
The balance in Beth's checking account = $75.00
She must deposit enough money in her account to be able to pay the electric bill, which is = $110.00
So we have to subtract 75 from 110 to get how much more money she needs to deposit the electric bill.
$110.00 - $75.00= $35.00
She should deposit $35.00 in her account.
When solving negative one over five -1/5 (x − 25) = 7, what is the correct sequence of operations
Answers
The solution would be like this for this specific problem:
[tex]\left( { - 5} \right) \cdot \left( { - \frac{1}{5}} \right) \cdot \left( {x - 25} \right) = 7 \cdot \left( { - 5} \right)[/tex]
[tex]\left( { - 5} \right) \cdot \left( { - \frac{1}{5}} \right) = 1[/tex]
The correct sequence of operations when solving negative one over five (x − 25) = 7 would be multiply each side by −5, and adding 25 to each side.
The proof that MNG ≅ KJG is shown.
Given: angle N and angle J are right angles; NG ≅ JG
Prove: MNG ≅ KJG
What is the missing reason in the proof?
the reflexive property
ASA
AAS
the third angle theorem
Answers
The line [tex]\mathbf{\overline{MK}}[/tex] is a bisector of the line [tex]\mathbf{\overline{JN}}[/tex], and both lines form part of
ΔMNG and ΔKJG.
Correct response:
The missing reason in the proof is; ASAMethod used to prove ΔMNG ≅ ΔKJG, and find the missing reasonA two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{NG}[/tex] ≅ [tex]\overline{JG}[/tex] 1. Given (hash marks representing equal length)
2. ∠N and ∠J are right angles 2. Given (symbol for right angle)
3. ∠MGN ≅ ∠KGJ 3. Vertical angle are congruent (theorem)
4. ∠N ≅ ∠J 4. Right angles are (all) congruent
5. ΔMNG ≅ ΔKJG 5. Angle-Side-Angle, ASA, congruency rule
The missing reason in the proof is; ASAAccording to the ASA congruency rule, if two angles and the included
side of one triangle are the same to two angles and the included side of
another triangle, the two triangles are congruent.
∠N, side [tex]\mathbf{\overline{NG}}[/tex]∠MGN in ΔMNG are congruent to ∠J, side [tex]\mathbf{\overline{JG}}[/tex]∠KGJ in ΔKJG
Therefore;
ΔMNG ≅ ΔKJG by ASA congruency ruleLearn more about ASA postulate here:
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(4.04 LC)
Which equation represents a linear function?
Equation 1: y3 = 2x + 1
Equation 2: y = 3x + 1
Equation 3: y = 5x2 − 1
Equation 4: y = 4x4 − 1
A. Equation 1
B.Equation 2
C. Equation 3
D. Equation 4
Answers
B. Equation 2
Given: The universal set = {all animals}; A = {hogs}; B = {cows}; C = {horses}; D = {foals}; E = {mares}. Click on the diagram until you find the one that correctly represents the expression. (Note: mares are female horses, foals are baby horses).
Answers
Next, because hogs, cows and horses are different animals, they will all be in separate, non-overlapping sets.
Finally, D and E are types of horses so they will be complete contained within set C. Note that a baby horse may either be male or female, so the set D and set E will overlap.
Use 1% or 10% to estimate 8% of 310.
Answers
To estimate the 8% of 310, we use 10% method since 8 when rounded off is equals to 10.
The 10% of a number can simply be obtained by moving the decimal place one point to the left.
Therefore using the 10% method, the 8% of 310 is approximately 31.0
Answer: 10% = 31.0
A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs. To the nearest whole percent, what is the probability that a car is an SUV, given that it is white? 9% 15% 21% 57%
Answers
Answer: 15 % ( approx)
Step-by-step explanation:
Let S represents the event that the car is SUV.
And W is the event that the car is white.
Then According to the question,
23% of the cars manufactured last year were SUVs,
Thus, the probability of SUV Car,
[tex]P(S)= \frac{23}{100} =0.23[/tex]
Similarly Probability that the car is white,
[tex]P(W)= \frac{13}{100} =0.13[/tex]
And, the probability that cars manufactured were white SUVs,
[tex]P(S\cap W)= \frac{2}{100} =0.02[/tex]
Thus, the probability that a car is an SUV, given that it is white,
[tex]P(\frac{S}{W} )= \frac{P(S\cap W)}{P(W)} = \frac{0.02}{0.13}[/tex] = 0.15384615384= 15.384615384 % ≈ 15 %
Therefore, Option B is correct.
WILL GIVE A BRAINLIEST!! PLEASE HELP!!
Which of the following parent functions has the most restricted domain?
A.
y=1/x
B.
y=x^2
C.
y=square root x (i couldnt find the symbol)
D.
y = |x|
Answers
The chairlift at a ski resort rises a total of 2600 feet from where it starts. The angle of elevation is about 22.3. How far do riders travel on the lift?
Answers
make sure your calculator is in Degree mode.
ABC is similar to pqr. Ab corresponds to pq and bc corresponds to qr. if the length of ab is 9 units the length of bc is12units the length of ca is 6units and the length of pq is 3 units then the length of qr is ? Units and the length of rp is ? Units
Answers
if you multiply QP which equals 3, by 3, then you would get 9.
So you would divide BC by 3. 12/3= 4
Then divide AC by 3. 6/3=2.
Answer:
[tex]QR=4\ units[/tex]
[tex]RP=2\ units[/tex]
Step-by-step explanation:
we know that
If two triangles are similar
then
the ratio of their corresponding sides are equal
In this problem
triangle ABC is similar triangle PQR -------> given problem
so
[tex]\frac{AB}{PQ}=\frac{CA}{RP}=\frac{BC}{QR}[/tex]
we have
[tex]AB=9\ units, PQ=3\ units,CA=6\ units,BC=12\ units[/tex]
Find the length of side QR
[tex]\frac{AB}{PQ}=\frac{BC}{QR}[/tex]
substitute the values and solve for QR
[tex]\frac{9}{3}=\frac{12}{QR}[/tex]
[tex]QR=12*3/9=4\ units[/tex]
Find the length of side RP
[tex]\frac{AB}{PQ}=\frac{CA}{RP}[/tex]
substitute the values and solve for RP
[tex]\frac{9}{3}=\frac{6}{RP}[/tex]
[tex]RP=6*3/9=2\ units[/tex]
If ABCDE is translated 3 units to the right and 4 units down, what will happen to the polygon?
Answers
B] It will move but won't change shape or size.
When polygon ABCDE is translated 3 units to the right and 4 units down, its shape and size remain unchanged, but its position on the coordinate plane changes, maintaining the same orientation and angles.
Explanation:If a polygon ABCDE is translated 3 units to the right and 4 units down, the shape and size of the polygon will remain the same, but its position will change. Each vertex (point) of the polygon will move 3 units to the right on the x-axis and 4 units down on the y-axis. This type of transformation is known as a translation, which is a slide of the entire figure in a specific direction. As a result, the translated polygon will maintain the same orientation and angles; it will simply be in a different location on the coordinate plane.